That 1988 paper was a modification of the previous design,as an attempt to address criticisms, but thank you for the cite.
It is important to realize that relations are abstract data structures that we treat like sets, not objects we constructed from sets.
If you want to do the set specific approach, reviewing any books on basic set theory and their intentional and extensional set definitions with show your argument is confusing the map for the territory.
The set operations applied to relations produce relations or relations of relations.
Same in material set theory, excluding membership, the only set operation that isn't predicated, this operating on the set, and not opening it up to act on its members.
While the platonic ideal may seem to make it seem different, urelements/atoms/individuals are not what those operations are acting on.
That is what made ZF(C) different.
Remember that Codd was targeting the hierarchical model, records etc...
While the other camp was targeting the network model, specifically using lists.
From the platonic view, uniqueness is a trivial, syntax property, you make that choice, and it has costs.
The typical example is I am a person who lives in (a member) the US, and the US is a member of the UN. Yet I am not a member of the UN.
Similar challenges are why Codd added Recursive CTEs to capture some of the expressiveness of the network model, which OOP is related to.
The problems Codd was targeting in your cite were mostly addressed post SQL99 with the addition of structural data options, specifically challenges with foreign keys.
The intersection of a column and a row being a field, which maps to cobol record concepts is why tables and relations are equal.
If you look at the 1970 paper I provided above, you can see where his concrete implementation using arrays calls out it isn't equal and requires distinct entries.
Note the link to the author's page allowing you to download the Alice book in its entirety works now.
I encourage you to get it.
The concept of a relation as a data structure is far more abstract than it seems.
Yes Codd did attempt to become more prescriptive later, but there is a reason no one exactly implemented it, just like platonic ideals it doesn't really work for real world needs, nor is it required for ACID transactions.
But the relation is still a binary operations that is equivalent to a table.